# How to find all roots of the quintic using the Bring radical

Finding one root $x_1$ of the quintic equation $x^5 + x = -a$ by using the Bring radical is described on Wikipedia.

The root is $x_1 = -a +a^5 -5a^9+35a^{13}+ \ldots$ , and it is found by reversion of the Taylor series for $f(x) = x^5 + x$.

How do we find the other roots of this quintic in series representation?